WASHINGTON (Reuters) - An adult-film actress who claims she had sex with Donald Trump before he was president said on Sunday she had been threatened in 2011 while in a parking lot with her infant daughter to discourage her from discussing the relationship.

Stormy Daniels, whose real name is Stephanie Clifford, told CBS News' "60 Minutes" that she was on her way to a fitness class with her child when an unknown man approached her, according to a transcript of the interview released on Sunday.

"And a guy walked up on me and said to me, 'Leave Trump alone. Forget the story.' And then he leaned around and looked at my daughter and said, 'That’s a beautiful little girl. It'd be a shame if something happened to her mom.' And then he was gone," Daniels said.

Daniels sued the president on March 6, stating Trump never signed an agreement for her to keep quiet about an "intimate" relationship between them.

White House aides did not respond immediately to requests for comment after the interview aired.

Trump did not respond to reporters' shouted questions about whether he would watch the interview when he returned to the White House from Florida on Sunday evening.

Daniels' appearance represented back-to-back trouble for Trump after an interview broadcast last week on CNN with former Playboy model Karen McDougal, who described a 10-month-long affair with Trump starting in 2006.

Trump would have been married to his wife, Melania, during both the alleged extramarital relationships. The first lady accompanied him this weekend to his Florida golf club. A White House spokeswoman said Melania stayed behind, as is her custom during their son's school holiday.

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Daniels told "60 Minutes" she and Trump had had sexual relations only once, but that she had seen him on other occasions and he had kept in touch with her.

She said she was not attracted to Trump, who was 60 at the time. Daniels was 27 in 2006.

The White House has denied he had an affair with Daniels, although Trump's lawyer Michael Cohen said he paid her $130,000 of his own money during the 2016 presidential election campaign.

The payment could pose a legal problem. Watchdog groups have filed complaints with the Department of Justice and Federal Election Commission, saying that it may have violated campaign finance law by exceeding the limit on the size of a contribution.

Cohen, who has denied that there was an affair, has not explained why he made the payment or said whether Trump was aware of it.

After the interview screened, Cohen's lawyer Brent Blakely wrote to Daniels' attorney to say she made false and defamatory comments, "namely that he (Cohen) was responsible for an alleged thug who supposedly visited" and threatened her.

"In truth, Mr. Cohen had absolutely nothing whatsoever to do with any such person or incident, and does not even believe that any such person exists, or that such incident ever occurred," Blakely said in the letter.

Daniels and her attorney would not discuss in the interview whether they had text messages or other materials that might verify her story.

She was asked why she repeatedly signed statements denying the relationship with Trump, and acknowledged that there could be questions about her credibility.

"I felt intimidated and ... honestly bullied. And I didn't know what to do. And so I signed it," Daniels said.

Asked why viewers could be confident now that she was telling the truth, she said: "Cause I have no reason to lie. I'm opening myself up for, you know, possible danger, and definitely a whole lot of s***," she said.

(Reporting by Patricia Zengerle; Additional reporting by David Lawder, Sarah Lynch, Steve Holland and Jim Oliphant in WASHINGTON, and Karen Freifeld in NEW YORK; Editing by Caren Bohan, Grant McCool and Paul Tait)